GATE CSE 2020 | GA | Question: 9

Question

Two straight lines are drawn perpendicular to each other in $X-Y$ plane. If $\alpha$ and $\beta$ are the acute angles the straight lines make with the $\text{X-}$ axis, then $\alpha + \beta$ is ________.

• A. $60^{\circ}$
• B. $90^{\circ}$
• C. $120^{\circ}$
• D. $180^{\circ}$

Comments

X=0 is a line perpendicular to y plane.

Y=0 is a line perpendicular to x plane.

Acute angle made by x=0 with x axis=90

Acute angle made by y=0 with x axis=0

 

So, answer is 90+0=90

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Answer Here!   

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Can someone answer one doubt? According to the question, both lines make acute angles with the x-axis, so this acute angle consideration is not given. If we consider any two perpendicular lines except x=0 and y=0, one line will always make an obtuse angle with the x-axis, considering anticlockwise angle consideration; the same way we consider in slope calculation, but in general, any line which intersect x axis will always have one acute angle if we want to take only acute angles.

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But 0 is not considered as an Acute angle

Answer 1

Here, we can clearly see that Two Lines $L_{1}$ and $L_{2}$ are intersecting each other at the right angle.

Now we also know that in a triangle, the sum of three angles is 

• $\angle A + \angle B + \angle C=180^{\circ}$ 
• $\alpha +\beta + 90^{\circ}=180^{\circ}$ 
• $\alpha + \beta = 90^{\circ}$

The answer is (B).

Comments

The graph can have one more case where both the lines make V shape on X-axis i.e. intersect each other on X-axis

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Considering the case you have mentioned in the above comment,

if both the lines make V shape on X-axis then also the sum of both acute angles and the right angle(since both lines are perpendicular to each other) equals 180 degrees i.e., 

α + β + 90 = 180

then α + β = 90.

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Yes, I just wanted to say that this case should also be added in order to make the answer complete.

Answer 2

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L1 and L2 are two perpendicular lines(i.e. 90°).

let say lines L1 and L2 are making acute angles with the x-axis i.e. α and y-axis i.e. β respectively.

therefore, by Angle Sum Property of Triangles in the triangle with 

α+β+90° = 180°

α+β = 90° .

option B.

 

Answer 3

as the two lines are perpendicular to each other so

90+a+b=180

or, a+b=180-90=90

ans..B

Answer 4

straight line make 180* with the x-axis

a+b+90=180

a+b=90

Answer 5

B